Regressor Dynamics

Requirements Clarification & Assessment

1. Understanding the Question

   • The question asks for an analytical comparison between regressing Y on X and X on Y, specifically focusing on the relationship between their respective R-squared values.
   • Key concepts involved include linear regression, R-squared values, and Pearson's correlation.

2. Key Concepts

   • Linear Regression: A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation.
   • R-squared (R²): A statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable in a regression model.
   • Pearson's Correlation (r): A measure of the linear correlation between two variables X and Y, ranging from -1 to 1.

3. Analytical Derivation Requirement

   • Derive the connection between the R-squared values when regressing Y on X and X on Y.
   • Understand how the slope and correlation coefficient play a role in determining these R-squared values.

4. Assumptions

   • The data follows a linear relationship.
   • The variables X and Y are continuous and have no missing values.
   • The regression models are simple linear regressions (one independent variable).